Understanding the topological properties of band insulator and interacting topological insulator
is one of the most fundamental and challenging tasks in the studies of condensed matter materials and ultracold atomic gases [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}.
As a highly controllable and disorder-free system, ultracold atoms in optical lattices provide
a powerful platform for quantum simulation of topological states of matter [5]}, [7]}, [8]}.
One of the most basic and easiest models in describing band topology is the celebrated Su-Schrieffer-Heeger (SSH) model [12]},
which has been experimentally implemented with ultracold atoms in one-dimensional (1D) dimerized optical
superlattices [13]}, [14]}, [15]}, [16]}, [17]}.
